Chivas USA remains four points out of the playoff picture after Angel scored the equalizer in the closing minutes.
Justin Mapp started the scoring off in the 59th for Philadelphia, which moved into second place in the Eastern Conference.
Angel scored on a header following a cross from Michael Lahoud, who was subbed into the game in the 74th minute. It was Angel's seventh goal of the season.
Chivas USA remains four points out of the final wild-card spot.